C₃₇×#3069 #17991887

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3068
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3069

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₇	C₂×#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 4 generators on 69 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39,44,49)(40,50,52,61)(41,55,57,63)(42,48,43,47)(45,54,60,53)(46,58,62,56)(51,65,66,59)(64,68,69,67);(38,40,42,53,44,52,43,54)(39,45,47,50,49,60,48,61)(41,51,56,67,57,66,58,68)(46,59,55,64,62,65,63,69);(38,41)(39,46)(40,51)(42,56)(43,58)(44,57)(45,59)(47,55)(48,63)(49,62)(50,64)(52,66)(53,67)(54,68)(60,65)(61,69);(40,52)(45,60)(50,61)(51,66)(53,54)(59,65)(64,69)(67,68)

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#24421, C₃₇×#24423, C₃₇×#24474, …
maximal normal subgroup of	C₃₇×#24421, C₃₇×#24423, C₃₇×#24474, …
maximal quotient of	C₃₇×#19163, C₃₇×#19164, C₃₇×#19167, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1801);

C37×#3069 #17991887